Equivalent classes of closed three-level systems

In recent years a significant amount of research in quantum optics has been devoted to the analysis of atomic three-level systems and for many physical quantities the same effects have been predicted for different configurations. These configurations can be split into essentially two classes. One for which the system contains a metastable state and another where the system has two close-lying levels and coherence effects become important. We demonstrate when and why for a wide range of parameters these two classes are in fact equivalent for many important physical quantities. A unified picture underlying a large body of work on these categories of atomic three-level systems is presented and applied to some examples.